Argument: Polygamous divorce is a legal nightmare in dividing children and property

From Debatepedia

"Legalize Polygamy?". New York Times letter to editor. March 14, 2006 - "Divorce in a polygamous family would be a legal nightmare. If a polygamous family split, how would the community property be divided? What about custody and support of children produced in that union? A situation is easy to visualize where the child of a working wife is raised entirely by a non-working wife who has no legal standing with respect to the child."

Not sure why polygamy would be harder than normal marriages. Worst case scenario you would have to do DNA test to determine parenthood? Women get to keep the children usually, just like normal marriages. Women each get a portion of the communities property on their own, just like they received when they were part of the group, right? What is the difference?